摘要：
In the past several decades, many papers involving the stability and Hopf bifurcation of delayed neural networks have been published. However, the results on the stability and Hopf bifurcation for fractional order neural networks with delays and fractional order neural networks with leakage delays are very rare. This paper is concerned with the stability and the existence of Hopf bifurcation of fractional order BAM neural networks with or without leakage delay. The Laplace transform, stability and bifurcation theory of fractional-order differential equations and Matlab software will be applied. The stability condition and the sufficient criterion of existence of Hopf bifurcation for fractional order BAM neural networks with delay (leakage delay) are established. It is found that when the sum of two delays (leakage delay) crosses a critical value, then a Hopf bifurcation will appear. The obtained results play an important role in designing neural networks. Also the derived results are new and enrich the bifurcation theory of fractional order delayed differential equations.
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Yuan, Shuai] Cent South Univ, Sch Math & Stat, Changsha 410083, Peoples R China.
通讯机构：
[Changjin Xu] G;Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, PR China
关键词：
Complex-valued neural networks;Hopf bifurcation;Leakage delay;Stability;Fractional order
摘要：
During the past decades, integer-order complex-valued neural networks have attracted great attention since they have been widely applied in in many fields of engineering technology. However, the investigation on fractional-order complex-valued neural networks, which are more appropriate to characterize the dynamical nature of neural networks, is rare. In this manuscript, we are to consider the stability and the existence of Hopf bifurcation of fractional-order complex-valued neural networks. By separating the coefficients and the activation functions into their real and imaginary parts and choosing the time delay as bifurcation parameter, we establish a set of sufficient conditions to ensure the stability of the equilibrium point and the existence of Hopf bifurcation for the involved network. The study shows that both the fractional order and the leakage delay have an important impact on the stability and the existence of Hopf bifurcation of the considered model. Some suitable numerical simulations are implemented to illustrate the pivotal theoretical predictions. At last, we ends this article with a simple conclusion. (C) 2020 Elsevier Ltd. All rights reserved.
摘要：
The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Applying Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential systems, we establish a new sufficient condition to ensure the stability and the emergence of Hopf bifurcation of the addressed fractional-order BAM neural networks with multiple delays. The research indicates that the delay has a vital effect on the stability and the appearance of Hopf bifurcation of fractional-order BAM neural networks. Computer simulations are put into effect to test the effectiveness of the theoretical findings. It is shown that when the sum of time delays crosses some critical values, the stability of networks loses and Hopf bifurcation will happen. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
摘要：
In this manuscript, fuzzy delayed cellular neural networks with impulse are studied. Applying time scale calculus knowledge, mathematical inequalities and constructing Lyapunov function, we establish a sufficient criterion that guarantees the existence and exponential stability of anti-periodic solutions for fuzzy delayed cellular neural networks with impulse. In addition, an example with its numerical simulations is given to illustrate our theoretical predictions.
关键词：
cancer treatment;chemotherapy model;delay;fractional order;Hopf bifurcation;stability
摘要：
Cancer is one of the most serious diseases in the world. The investigation on cancer treatment has attracted great attention from medical workers, mathematical researchers, and scholars in various fields. To understand the intrinsic characteristics of cancer, numerous scholars have established cancer treatment models and discussed the dynamical properties. However, the main work of many scholars only focuses on the integer-order cancer treatment models, while the study on fractional-order ones is quite a few. In the present article, on the basis of previous publications, we will put up a new fractional-order chemotherapy model with two different delays. By applying the stability theory and the Hopf bifurcation of fractional-order differential equations, we obtain a series of new stability criteria of the involved model and some sufficient conditions to ensure the existence of Hopf bifurcation of the involved model. Furthermore, the impact of two different delays and the fractional order on the stability and the emergence of Hopf bifurcation of involved model is presented. To illustrate the validity of analytical predictions, we perform computer simulations with Matlab software. The theoretical results in the manuscript are innovative and play an important role in cancer treatment.
摘要：
In this paper, we propose a new fractional-order financial model which is a generalized version of the financial model reported in the previous publications. By applying a suitable time-delayed feedback controller, we have control for the chaotic behavior of the fractional-order financial model. We investigate the stability and the existence of a Hopf bifurcation of the fractional-order financial model. A new sufficient condition that guarantees the stability and the existence of a Hopf bifurcation for a fractional-order delayed financial model is presented by regarding the delay as bifurcation parameter. The investigation shows that the delay and the fractional order have an important effect on the stability and Hopf bifurcation of involved model. Some simulations justifying the validity of the derived analytical results are given. The obtained results of this article are innovative and are of great significance in handling the financial issues.
摘要：
This manuscript mainly deals with quaternion-valued neural networks (QVNNs) with delays and inertial term. Using Wirtinger inequality and coincidence degree theory, a new sufficient criterion to ensure the existence of antiperiodic solution of involved quaternion-valued neural networks is derived. With the aid of Lyapunov function, we discuss the exponential stability of antiperiodic solutions to quaternion-valued neural networks. Numerical simulations are presented to illustrate the established theoretical findings.
关键词：
Cellular neural networks;Almost automorphic solution;Exponential stability;Leakage delay;Neutral type delay
摘要：
In this paper, cellular neural networks (CNNs) with neutral type delays and time-varying leakage delays are investigated. By applying the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, a set of sufficient conditions which ensure the existence and exponential stability of almost automorphic solutions of the model are obtained. An example with its numerical simulations is given to support the theoretical findings. (C) 2020 The Authors. Published by Atlantis Press SARL.
摘要：
In the present work, we mainly focus on shunting inhibitory cellular neural networks (SICNNs) involving leakage delays and proportional delays. By applying the inequality technique, a novel sufficient criterion to ascertain the convergence of every solution of SICNNs with leakage delays and proportional delays is derived. Simulation results are delineated to substantiate the correctness of our theoretical findings. Up to now, very few scholars deal with the neural networks with leakage delays and proportional delays. The derived conclusion of this work is a novelty and supplements several earlier works.
摘要：
The paper deals with the stability and bifurcation analysis of a class of simplified five-neuron bidirectional associative memory neural networks with four delays. By discussing the characteristic transcendental equation and applying Hopf bifurcation theory, some sufficient conditions which guarantee the local stability and the existence of Hopf bifurcation of the neural networks are established. With the aid of the normal form theory and center manifold theory, we obtain some specific formulae to determine the stability and the direction of the Hopf bifurcation. Computer simulations are implemented to explain the key mathematical predictions. The paper ends with a brief conclusion.
摘要：
In this paper, a delayed Nicholson's blowflies model with a linear harvesting term is investigated. By transforming the model into an equivalent integral equation, and applying a fixed point theorem in cones, we establish a sufficient condition which ensure the existence of positive almost periodic solutions for the Nicholson's blowflies model. The results of this paper are completely new and complement those of the previous studies. The approach is new.
